The invention relates to a method and to an apparatus for determining a deviation of an actual shape from a desired shape of an optical surface. Furthermore, the invention relates to a method of producing an optical element. This type of apparatus is described, for example, in WO 2006/077145 A2. This apparatus comprises an interferometer for producing a measuring wave, the wavefront of which is hereupon adapted to the desired shape of the optical surface. The wavefront of the adapted measuring wave is analysed interferometrically after reflection on the optical surface, and the deviation of the actual shape of the optical surface from the desired shape of the latter is thus determined.
The optical element with the optical surface is, for example, an optical component such as for example a lens or a mirror. These types of optical component are used in optical systems, such as for example a telescope used in astronomy or in an imaging system as used in lithographic processes. The success of this type of optical system is substantially determined by a precision with which the optical components of the latter can be produced and then be processed, such that the surface forms of the latter respectively correspond to a desired form which was specified by a designer of the optical system when designing the latter. Within the framework of this type of production it is necessary to compare the form of the processed optical surfaces with the desired form of the later, and to determine any differences and deviations between the finished surface and the desired surface. The optical surface can then be processed in those regions where differences between the processed surface and the desired surface exceed, for example, pre-specified threshold values.
Generally, interferometers are used for very high precision measurements on optical surfaces. The conventional interferometer arrangement for measuring an optical surface typically comprises a coherent light source and interferometer optics in order to produce a measuring light beam which strikes the surface to be measured such that wavefronts of the measuring light have at locations of the surface to be measured respectively a same form as the desired form of the surface to be measured. In this type of situation the light of the measuring light beam strikes each location of the surface being measured essentially orthogonally and is then reflected back from the latter in itself. The reflected back measuring light is then overlaid with reference light which has been reflected by a reference surface. Deviations between the form of the surface measured and its desired form can then be established from interference thus produced.
Whereas spherical wavefronts can be produced for measuring spherical optical surfaces with a relatively high degree of precision by using conventional interferometer optics, advanced techniques are required in order to produce measuring light beams the wavefronts of which are aspherical so that the measuring light at each location of an aspherical optical surface to be measured strikes the latter orthogonally. In order to produce these types of measuring light beam optics are used which are called zero lenses, K systems or compensators. Background information with regard to these zero lenses or compensators can be found in Chapter 12 of the text book by Daniel Malacara, Optical Shop Testing, 2nd edition, Wiley interscience Publication (1992).
This type of compensator for producing aspherical wavefronts can contain one or more refractive optical elements, such as for example lenses or one or more diffractive optical elements, such as for example diffraction gratings or holograms. Background information with regard to the use of diffraction gratings in interferometer optics can be found in Chapters 15.1, 15.2 and 15.3 of the text book by Daniel Malacara.
This diffraction grating can be, for example, a computer-generated hologram (CGH) which is produced by the structure of the interferometer being simulated by a suitable calculation method, such as for example a ray tracing method, and a phase function of the diffraction grating being calculated here such that the latter has a desired function in the optical path of the interferometer arrangement. This can then be produced from the calculated phase function of the diffraction grating.
Methods for producing these types of computer-generated hologram include, for example, writing the grating with a laser beam or an electron beam with the aid of lithographic steps.
One problem here is that the effect of a diffraction grating with high line densities with which a grating period is not substantially greater than the wave length of the measuring light used is difficult to predict with a simple diffraction theory and moreover production-dependent parameters of the grating, such as for example the base height, edge steepness and the rounding of edges influence the effect of the grating. Such influences are not defined by the grating period alone, and in the present technical field are also called rigorous effects.
From WO03/048715 A1 an interferometer arrangement with a CGH is known which produces two types of wavefront, one type of wavefront being aspherical wavefronts which are used for measuring an aspherical optical surface, whereas the other type of wavefront is substantially spherical wave-fronts with which a calibration block is measured. From the measurement of the calibration block, conclusions can be drawn regarding the effect of the hologram upon the measuring light which can then be used when analysing the measurement on the aspherical optical surface.
The so-called rotation averaging method has proven to be advantageous for the most precise interferometric measurements. The rotation averaging method is however only suitable for measuring rotationally symmetrical surfaces. Free-form surfaces without rotational symmetry can not be measured using the rotation averaging method. With strongly decentred off-axis aspheres a measurement in a number of rotational positions can only be obtained with clear disadvantages. An off-axis asphere is understood as meaning a basically rotationally symmetrical asphere which has a surface region to be measured which is strongly decentred with regard to its axis of symmetry. For the measurement in a number of rotational positions with this type of off-axis asphere the test optics must not only be designed for the off-axis useful region to be tested, but in fact for the rotationally symmetrical parent asphere, which leads to reduced local resolution.